Aggregation of monotone reciprocal relations with application to group decision making

This paper is composed of two complementary parts. The first part is a formal investigation into the interplay of properties of reciprocal relations, how monotonicity relates to some natural and intuitive properties, including stochastic transitivity. The goal is to aggregate monotone reciprocal relations on a given set of alternatives. Monotonicity is expressed w.r.t. a linear order on the set of alternatives. The second part is a practical protocol to both determine the best fitting linear order underlying the alternatives, and construct a reciprocal relation monotone w.r.t. it. We formulate the problem as an optimization problem, where the aggregated linear order is that for which the implied stochastic monotonicity conditions are closest to being satisfied by the distribution of the input monotone reciprocal relations. We show that if stochastic monotonicity conditions are satisfied, a monotone reciprocal relation is easily found on the basis of the (possibly constructed) stochastically monotone reciprocal distributional relation.     

二项式系数倒数级数恒等式

利用已知级数,通过裂项构造出一批新的二项式系数倒数级数,它们的分母分别含有1到4个奇因子与二项式系数的乘积表达式.所给出二项式系数倒数级数的和式是封闭形的.     

CFL condition,Boltzmann's H‐theorem,Onsager reciprocal relations and beyond

In this article, we show that the classical CFL condition from numerical analysis, Boltzmann's H‐theorem from kinetic theory and Onsager reciprocal relations from nonequilibrium thermodynamics are all related to some structural stability conditions for nonhomogeneous systems of first‐order partial differential equations. By doing this, we briefly review our previous works on first‐order partial differential equations. Copyright © 2013 John Wiley & Sons, Ltd.     

A least deviation method for priority derivation in group decision making with incomplete reciprocal preference relations

In this paper, based on the transfer relationship between reciprocal preference relation and multiplicative preference relation, we proposed a least deviation method (LDM) to obtain a priority vector for group decision making (GDM) problems where decision-makers' (DMs') assessments on alternatives are furnished as incomplete reciprocal preference relations with missing values. Relevant theorems are investigated and a convergent iterative algorithm about LDM is developed. Using three numerical examples, the LDM is compared with the other prioritization methods based on two performance evaluation criteria: maximum deviation and maximum absolute deviation. Statistical comparative study, complexity of computation of different algorithms, and comparative analyses are provided to show its advantages over existing approaches.     

Design method of reusable reciprocal invisibility and phantom device

Reusable reciprocal invisibility and phantom device is proposed and designed based on multi-folded transformation optics and equivalent components. In comparison with the reported reciprocal invisibility cloaks, the material parameters of the device presented here are homogeneous, and the hiding of the target object does not require any "anti-object" at all, which dramatically breaks through the limitations of the "anti-object" design in previous reciprocal cloak design. Perfectly illusion effect is also found by reasonably setting the material parameters of the restored medium of the device, which can be used to confuse detection radars while hiding target objects. Last but not least, the proposed device has an open structure, which enables the target object enclosed by the device to perform material exchange and simplex transfer of information with the outside world through open channels. In other words, the proposed device has a reusable function, enabling stealth or phantom of new target objects without changing any parameters of the device.